Bayern equalled their biggest Champions League win as they reached their eighth quarter-final in 11 seasons - and it was never in doubt after Kucher's early dismissal.

The only time the Germans have been eliminated from a European competition after drawing the first leg away 0-0 was in 1981.

Back then, they fell in a European Cup semi-final to Liverpool on the away goals rule after drawing 1-1 at home in the second leg, but Bayern have won on the other six occasions.

Thomas Muller has 26 Champions League goals, the joint-highest total of any German player

From the moment Kucher rashly opted to slide in on Mario Gotze inside the penalty area within the first three minutes, it was one-way traffic for the five-time European Cup winners, who last lifted the trophy in 2013.

A red card was followed by Muller's inevitable calm finish from the spot - and that was that as far as the contest was concerned.

By half-time, Bayern had enjoyed 79% of possession, with 15 shots on goal compared to Shakhtar's one.

Boateng's close-range finish, after Robert Lewandowski's close-range shot was blocked, doubled the lead, as Lewandowski, Robben and Muller all went close to inflicting further damage.

The Bundesliga champions had not lost at home since being thrashed by Real Madrid in last season's semi-final and they were in the mood for more goals.

Ribery drilled the ball in to the far post soon after the break and, minutes later, Muller fired in his second of the night after more good work from Ribery.

Goal!

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Goal! FC Bayern München 7, Shakhtar Donetsk 0. Mario Götze (FC Bayern München) right footed shot from the left side of the box to the bottom left corner. Assisted by Jerome Boateng with a through ball following a fast break.

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Corner, Shakhtar Donetsk. Conceded by Dante.

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Attempt missed. Robert Lewandowski (FC Bayern München) left footed shot from the left side of the box misses to the right. Assisted by Mario Götze with a through ball.

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Attempt missed. Viacheslav Shevchuk (Shakhtar Donetsk) left footed shot from outside the box is just a bit too high. Assisted by Fred.

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Attempt missed. Thomas Müller (FC Bayern München) left footed shot from the centre of the box is close, but misses to the right. Assisted by Sebastian Rode with a cross.

Substitution

Attempt missed. Fred (Shakhtar Donetsk) left footed shot from outside the box is high and wide to the left. Assisted by Douglas Costa.

Goal!

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Goal! FC Bayern München 6, Shakhtar Donetsk 0. Robert Lewandowski (FC Bayern München) right footed shot from the centre of the box to the bottom left corner. Assisted by Bastian Schweinsteiger with a through ball following a fast break.